Granular solids are a class of materials which generally have a resistance to deformation that is caused by a combination of interparticle friction, dilatant effects of grain rearrangement and cohesion, if it is present. The frictional nature of granular materials' resistance to deformation usually means that the effective shear strength of the bulk material increases with confining load. Because of this pressure-dependent deformation resistance, it is nearly impossible to push most granular materials down a pipe with a piston. An analysis to predict the stresses in storage silos by Janssen circa 1885 can be adapted, with only minor changes, to predict the stresses in a granular solid pushed in a pipe. Such an analysis shows that the resistance to pushing with a piston increases exponentially with the length of the slug being pushed. Primarily for this reason, methods which are commonly used to move fluids in pipes by creating a high pressure at one end of a pipe, do not work for ‘pumping’ granular solids through pipes. Generally, only mechanisms that create relatively short sections or slugs of granular material, and deliver a driving force to each slug separately, work to move granular materials through pipes. As a consequence, screw conveyors are one commonly used means of moving non-cohesive granular solids over modest distances. However, the design of screw conveyors has not changed a great deal since Greek mathematician and physicist Archimedes invented the screw conveyor in 235-240 B.C. aside from using improved materials and fabrication techniques and adding electricity as a power source.
For horizontal conveying or for gentle inclines (e.g., less than about 25 degrees), screw conveyors can be either in fully enclosed tubes or open-topped with a helical screw near the bottom of a U-shaped trough. The open-topped style conveyors generally operate at low rotation rates with granular material being pushed along the rising side of the screw faces, not unlike a bulldozer blade pushing material over the surface of the ground, except that the screw face is continuously moving up and the material is sliding down the face as it moves axially along the tube. For steeper inclinations, or vertical applications, fully enclosed tubes are employed and higher rotation rates are often used. The mechanism of motion of the granular material inside fully enclosed screw conveyors, with rapid rotation, is enhanced by the resistance to rotary or vortex motion of the bulk solid being provided by the total casing surface. In a vertical orientation, at high rotation rates, the typical motion of a granular solid follows a generally helical path of ‘opposite-hand’ from that of the screw driving the material. The granular solid slides continuously on both the outer wall and on the screw faces. The screw blades in conventional screw conveyors are typically in the shape of a helicoid with a pitch such that the slope of the screw surface, as measured from a plane perpendicular to the screw axis, varies from a value between 30 and 45 degrees next to the outer wall to something much steeper next to the central shaft of the screw. The wall friction of the tube, the angle of the screw face, the friction coefficient between the granular solid and the outer wall, and the friction with the screw face all contribute to proper functioning of conventional screw conveyors. The effect of the outer wall friction is enhanced at high rotation rates by the centrifugal force of the solid traveling along its helical path. The increase in outer wall normal force, due to the vortex motion of the solid, increases the friction force on the outer wall, which actually assists in the conveying action of the screw, albeit at the expense of somewhat higher energy loss due to overcoming the higher friction forces.
Screw conveyors are generally used with free flowing granular solids, and they are less reliable when used with cohesive powders, wet materials, or generally with materials that have the cohesive strength of wet sand (i.e., about 10 kPa) or greater. For such cohesive materials, the screw sometimes fills with the cohesive material along part of its length, and then the entire screw and filled material rotate around the axis, with the fill-material sliding on the outer wall as it travels circumferentially around the axis yet not moving axially along the tube. For this reason, screw conveyors are not always reliable in applications that may have highly variable material properties, as may be the case when the moisture content or temperature of the conveyed material varies from time to time, in such a manner as to exhibit significant cohesion under some conditions. The high rotation rates of fully enclosed tube screw conveyors allow them to be used with granular materials with a somewhat broader range of cohesion; however, they are still not a reliable method for material any more cohesive than typical wet sand. Accordingly, it would be desirable and useful to provide effective means for moving granular materials with a wide range of cohesive strength. Flow-assistance measures are sometimes used, with varying degrees of success, to transport cohesive materials in screw conveyors, such as external vibrators for dislodging the material and/or breaking up cohesive clumps. Such flow assistance measures are often difficult to design in such a manner that they provide reliable assistance uniformly along the entire length of the screw conveyor, and thus, are not a robust or versatile solution for conveying cohesive materials.
The original Archimedes screw was designed and used for water, and was used by the Egyptians to pump bilge water out of ancient sailing ships and for pumping irrigation water out of rivers or canals. Large-scale Archimedes water screws are used today in applications requiring rapid movement of large volumes of water, as in storm water runoff systems. Large-scale Archimedes screws can sometimes handle highly viscous fluids; however, as the size is scaled down, the ability of the Archimedes screw to convey highly viscous or cohesive fluids decreases significantly. Thus, for fluids, their use is most commonly restricted to low viscosity liquids, such as water.
During the 1980's researchers at Lawrence Livermore National Laboratory examined the flow behavior of granular solids in the inside of rapidly rotating horizontal and vertical cylinders and cones. The primary focus of those investigations were to study the flow of granular solids on the inner walls of rapidly rotating, horizontal axis conical sections, not unlike a conical megaphone which is rapidly rotating about its axis and has sand poured into the small end. In those studies, the sand formed an inner cone angle equal to its natural angle of repose measured from the axis of the rotating cone to the angle of the inner sand surface, independent of the actual angle of the rotating cone into which it was placed. Theoretical analyses and numerical simulations of granular material centrifuging on the inner walls of rotated horizontal and vertical cylinders were also part of that research. That work showed, that in order for a granular material to remain stationary on the inner wall of a rapidly rotating vertical pipe, the rate of rotation must be sufficient for the following two inequalities to both be satisfied,
                              ω          p          2                ⁢                  R          i                    g        >          1              tan        ⁢                                  ⁢                  ϕ          r                      ,            and      ⁢                          ⁢                                    ω            p            2                    ⁢                      R            i                          g              >          1              tan        ⁢                                  ⁢                  ϕ          w                      ,where ωp is the angular rotation rate (rad/s) of the pipe, Ri is the inner radius of the granular layer on the inside of the rotating pipe, g is the acceleration of gravity, φw is the wall friction angle between the pipe wall and the granular solid (i.e., the arctangent of the wall friction coefficient), and φr is the angle of repose of the granular material. For horizontal pipes, similar relations were obtained, except that sin φ replaced tan φ. Thus, for horizontal pipes the material will remain stationary with respect to the pipe wall, if the following two relations are satisfied,
                              ω          p          2                ⁢                  R          i                    g        >          1              sin        ⁢                                  ⁢                  ϕ          r                      ,            and      ⁢                          ⁢                                    ω            p            2                    ⁢                      R            i                          g              >                  1                  sin          ⁢                                          ⁢                      ϕ            w                              .      For typical material and wall properties this means that a horizontal pipe needs to rotate more than 40% faster than enough for the centrifugal force to just balance gravity at the inner surface of the granular material at the top of the cylinder in order to prevent any circumferential sliding or shearing of the rotating granular layer on the wall of the pipe. At slower rotation rates, gravity tends to cause a slight slowing and shearing deformation of the ‘rising’ material and a slight acceleration of the ‘falling’ material, at circumferential locations that would correspond to about the 10:30 o'clock and 1:30 o'clock positions, assuming an analog clock face is oriented perpendicular to the pipe's axis.
A rotating-casing screw conveyor was recently developed (U.S. Pat. No. 7,314,131 B2, Jan. 1, 2008) which utilizes a rotating cylindrical pipe and a stationary central helical screw. This “Olds Elevator” rotating-casing screw conveyor uses less energy under certain conditions in vertical conveying than conventional stationary-pipe screw-conveyors and is able to vertically-convey somewhat more-cohesive materials. The Olds Elevator conveyor has certain features, however, which limit its applicability. First, it functions well only in near-vertical orientations and does not convey solids well horizontally, or at shallow angles of inclination. Second, its energy-efficiency increases with the rotation rate of the pipe, as does the conveying mass flow rate, up until a certain maximum operating rotation rate is reached. At rotation rates beyond this optimum speed, the conveying efficiency very rapidly declines. This makes the Olds Elevator relatively efficient only at conveying rates which are at, or very close to, its maximum conveying capacity. At lower conveying rates its energy efficiency decreases significantly. Thus, it has a limited range of conveying rates over which it offers significant efficiency advantages over conventional screw conveyors. The present invention provides a broader range of operating conditions under which efficient conveying can be achieved.
In view of the foregoing, there is a need for improved techniques for mechanically conveying granular solids that can handle a wide range of materials and is efficient over a wide range of conveying rates.
Unless otherwise indicated illustrations in the figures are not necessarily drawn to scale.